A long solenoid of length 0.4 m carries a current of 5 A and produces a magnetic field of 4 10⁻³ T at its centre. The total number of turns on the solenoid is:

Step-by-step solution

The magnetic field at the centre of a long solenoid is given by: B = ₀ n I where n is the number of turns per unit length. Since n = N L , we can write: B = ₀ ( N L ) I Rearranging the formula to solve for the total number of turns N : N = B L ₀ I Substituting the given values ( B = 4 10⁻³ T , L = 0.4 m , I = 5 A , and ₀ = 4 10⁻⁷ T m/A ): N = 4 10⁻³ 0.4 4 10⁻⁷ 5 N = 10^4 0.4 5 = 4000 5 = 800 The total number of turns is 800 . Answer: 800